Michael C. Ferris

• University of Wisconsin–Madison

An increasing number of electric loads, such as hydrogen producers or data centers, can be characterized as carbon-sensitive, meaning that they are willing to adapt the timing and/or location of their electricity usage in order to minimize carbon footprints. However, the emission reduction efforts of these carbon-sensitive loads rely on carbon inte...

We formulate and compare optimization models of investment in renewable generation using a suite of social planning models that compute optimal generation capacity investments for a hydro-dominated electricity system where inflow uncertainty results in a risk of energy shortage. The models optimize the expected cost of capacity expansion and operat...

We study a competitive partial equilibrium in markets where risk-averse agents solve multistage stochastic optimization problems formulated in scenario trees. The agents trade a commodity that is produced from an uncertain supply of resources. Both resources and the commodity can be stored for later consumption. Several examples of a multistage ris...

In many applications, conservation organizations depend on one species to indicate the presence of another. While extensive research has gone into methods for selecting these indicator species, few studies have directly measured the performance of indicator species in guiding conservation actions. Here, we evaluated whether a small number of indica...

We present a mixed complementarity problem (MCP) formulation of continuous state dynamic programming problems (DP-MCP). We write the solution to projection methods in value function iteration (VFI) as a joint set of optimality conditions that characterize maximization of the Bellman equation; and approximation of the value function. The MCP approac...

We study demand-side participation in an electricity market for an industrial consumer of electricity, with some flexibility to reduce demand, and capable of offering interruptible load reserve. Our consumer is a price maker, and the impact of its actions in the market is modelled via a bi-level optimization problem. We have extended a standard mod...

Management decisions can be informed by near-real-time data streams to improve the economics of the farm and to positively benefit the overall health of a dairy herd or the larger environment. Decision support tools can use data management services and analytics to exploit data streams from farm and other economic, health, and agricultural sources....

In recent years, the power systems research community has seen an explosion of novel methods for formulating the AC power flow equations. Consequently, benchmarking studies using the seminal AC Optimal Power Flow (AC-OPF) problem have emerged as the primary method for evaluating these emerging methods. However, it is often difficult to directly com...

Assembly of power flow equations has traditionally begun from a nodal analysis formulation of the underlying transmission circuit behavior. Most power flow formulations encapsulate network constraints in the bus admittance matrix, $Y_{bus}$ . From a circuit perspective, this admittance representation restricts network elements to be voltage contr...

We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and (quasi-) variational inequalities, and computing solutions of them from modeling languages. We define a new set...

Assembly of power flow equations has traditionally begun from a nodal analysis formulation of the underlying transmission circuit behavior. Most power flow formulations encapsulate network constraints in the bus admittance matrix, Y bus. From a circuit perspective, this admittance representation restricts network elements to be voltage controlled;...

Textbook treatments of the power flow and related problems are almost universally based on the bus admittance matrix Y bus , representing a choice of nodal analysis for the circuit equations. Many texts further simplify their presentation by insisting that all network components be represented in equivalents that are interconnections of two-termina...

We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and (quasi-) variational inequalities, and computing solutions of them from modeling languages. We define a new set...

A hallmark of industrialization is the construction of dams for water management and roads for transportation, leading to fragmentation of aquatic ecosystems. Many nations are striving to address both maintenance backlogs and mitigation of environmental impacts as their infrastructure ages. Here, we test whether accounting for road repair needs cou...

Conservation practitioners face difficult choices in apportioning limited resources between rare species (to ensure their existence) and common species (to ensure their abundance and ecosystem contributions). We quantified the opportunity costs of conserving rare species of migratory fishes in the context of removing dams and retrofitting road culv...

Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off betwe...

Supplementary text containing Figures 1–30, Tables 1–10, and a list of supplementary data files available on GitHub. (PDF)

Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off betwe...

Typical formulations of the optimal power flow (OPF) problem rely on what is termed the "bus-branch" model, with network electrical behavior summarized in the Ybus admittance matrix. From a circuit perspective, this admittance representation restricts network elements to be voltage controlled and limitations of the Ybus have long been recognized. A...

Conservation planning aims to optimize outcomes for select species or ecosystems by directing resources toward high-return sites. The possibility that local benefits might be increased by directing resources beyond the focal area is rarely considered. We present a case study of restoring river connectivity for migratory fish of the Great Lakes Basi...

Structures that block movement of fish through river networks are built to serve a variety of societal needs, including transportation, hydroelectric power, and exclusion of exotic species. Due to their abundance, road crossings and dams reduce the amount of habitat available to fish that migrate from the sea or lakes into rivers to breed. The bene...

Social contracts about cars and computersNaming is a hard problem in scienceCommon naming problems in programming and modelingBlacklisting confusing keywords in simulations of biologyUniquified names by versioning or by hashingPerspectives on naming from the humanitiesOnline referencesMini survey on improving namesNaming forms: debugging tools for...

Names in programming are vital for understanding the meaning of code and big data. We define code2brain (C2B) interfaces as maps in compilers and brains between meaning and naming syntax, which help to understand executable code. While working toward an Evolvix syntax for general-purpose programming that makes accurate modeling easy for biologists,...

This paper examines three different formulations of AC optimal power flow problem, and compares performance of well-established, general purpose optimization algorithms for each, over different initial conditions. Polar power-voltage, rectangular power-voltage and rectangular current-voltage are formulated to evaluate ACOPF solution characteristic....

This paper concerns a model of Cournot-Nash-Walras (CNW) equilibrium where the Cournot-Nash concept is used to capture equilibrium of an oligopolistic market with non-cooperative players/firms who share a certain amount of a so-called rare resource needed for their production, and the Walras equilibrium determines the price of that rare resource. W...

We model three on-chip network design problems-memory controller placement, resource allocation in heterogeneous on-chip networks, and their combination-as mathematical optimization problems. We model the first two problems as mixed integer linear programs. We model the third problem as a mixed integer nonlinear program, which we then linearize exa...

Affine variational inequalities (AVI) are an important problem class that generalize systems of linear equations, linear complementarity problems and optimality conditions for quadratic programs. This paper describes PATHAVI, a structure-preserving pivotal approach, that can process (solve or determine infeasible) large-scale sparse instances of th...

Affine variational inequalities (AVI) are an important problem class that generalize systems of linear equations, linear complementarity problems and optimality conditions for quadratic programs. This paper describes PATHAVI, a structure-preserving pivotal approach, that can process (solve or determine infeasible) large-scale sparse instances of th...

Conservation planning is designed to optimize conservation actions when only limited resources are available for managing habitats and mitigating threats, and excels at selecting reserve networks that protect the largest number of species. However, the spatial optimization of the protection of multiple species can be complicated by interactions amo...

We propose a bi-level optimization model for demand response in organized wholesale energy markets. In this model, the lower level performs the economic dispatch of energy and generates the price and the upper level minimizes the total amount of demand response subject to a net benefit requirement. In an economic sense, demand response is a trade o...

Agricultural lands have experienced rapid changes during the last decade. In the absence of preventative crop change policies, these changes can affect multiple ecosystem services simultaneously. The objective of this paper is to describe a web-based spatial decision support system (SDSS), which we call the SmartScape™, that helps policymakers to e...

The correspondence of competitive partial equilibrium with a social optimum is well documented in the welfare theorems of economics. These theorems can be applied to single-period electricity pool auctions in which price-taking agents maximize profits at competitive prices, and extend naturally to standard models with locational marginal prices. In...

We investigate a new class of congestion games, called Totally Unimodular Congestion Games, in which the strategies of each player are expressed as binary vectors lying in a polyhedron defined using a totally unimodular constraint matrix and an integer right-hand side. We study both the symmetric and the asymmetric variants of the game. In the symm...

We propose an extended bidding structure to allow more realistic demand characteristics and behaviors to be expressed via flexible bids. In today's ISO-run energy markets, demand bid formats are all separable over time. However, a significant and growing segment of demand can be shifted across time and therefore has no way to bid its true valuation...

After the day-ahead market is cleared and before the real-time market is started, Independent System Operator (ISO) uses a Reserve Adequacy Assessment (RAA) process to determine supplemental unit commitments to meet the hourly forecasted load and reserve requirements for the next operating day. This paper presents a stochastic programming model for...

This paper models the security-constrained economic dispatch problem with post-contingency corrective actions. In the nonlinear AC setting, the model is a large-scale nonconvex problem and is difficult to solve. A novel solution approach is proposed to deal with the scale and nonconvexity issues separately and effectively. The key point is to appro...

Significance Societies around the world make massive investments in ecosystem restoration projects to mitigate habitat loss, conserve biodiversity, and boost ecosystem services. We use a return-on-investment framework to assess the value of coordinating restoration efforts in space and time to maximize ecological connectivity between the Laurentian...

We model post-contingency corrective actions in the security-constrained economic dispatch and consider multiple stages of rescheduling to meet different security constraints. The resulting linear program is not solvable by traditional LP methods due to its large size. We devise and implement a series of algorithmic enhancements based on the Bender...

Meter-scale subvertical strike-slip fault traces in the central Californian Sierra Nevada exhibit geometric complexities that significantly contribute to their mechanical behavior. Sections of faults that opened at depth channelized fluid flow, as evidenced by hydrothermal mineral infillings and alteration haloes. Thin sections show a variation in...

In this paper, we formulate a long-term planning model of transmission line expansion based on balancing investment cost and reducing consumer cost. We achieve this by formulating a hierarchical framework that is sensitive to different agents operating on different timelines, the relationships of which may be competitive, cooperative or somewhere i...

This technical report provides a brief introduction into different ways that the equations of motion associated with the Differential Variational Inequality (DVI) approach can be posed. Both the primal and dual forms are outlined along with a discussion on the relaxed formulations. Using the dual relaxed formulation a static analysis was performed...

Tributaries to the Great Lakes are highly fragmented by dams and road crossings that act as potential barriers to migratory fishes, restricting their access to historical riverine spawning grounds. The removal or modification of barriers can restore migratory pathways for these species, but removal costs and habitat gains differ markedly among pote...

Systematic, genome-wide loss-of-function experiments can be used to identify host factors that directly or indirectly facilitate or inhibit the replication of a virus in a host cell. We present an approach that combines an integer linear program and a diffusion kernel method to infer the pathways through which those host factors modulate viral repl...

This chapter serves two broad purposes. First, it provides a general overview of optimization techniques. Second, it provides a detailed treatment of how to model design problems as MILP including the selection and formulation of variables, constraints, objective functions, and some advanced techniques to reformulate nonlinearity into linearity. Fo...

A system and method for producing an intensity modulated arc therapy (“IMAT”) treatment plan are provided. A plurality of segmentations are generated, from which the IMAT treatment plan is determined. Apertures within each segmentation are ordered by minimizing the total leaf movement between pairs of segmentations in adjacent angles, during which...

Download Free Sample In the last few decades computer systems and the underlying hardware have steadily become larger and more complex. The need to increase their efficiency through architectural innovation has not abated, but quantitatively evaluating the effect of various choices has become more difficult. Performance and resource consumption are...

Background/Question/Methods Scientists in the DOE-funded Great Lakes Bioenergy Research Center (GLBRC) are constructing complex economic and ecological models to design sustainable bioenergy cropping systems. In the process, researchers must grapple with the economic and environmental tradeoffs associated with designing cropping systems that can...

Hydro-economic river basin models (HERBM) based on mathematical programming are conventionally formulated as explicit ‘aggregate optimization’ problems with a single, aggregate objective function. Often unintended, this format implicitly assumes that decisions on water allocation are made via central planning or functioning markets such as to maxim...

Yanchao Liu is a Ph.D. candidate of Industrial and Systems Engineering at the University of Wisconsin-Madison. He obtained his Master of Science degree in Industrial Engineering at the University of Arkansas in 2008. His research interest includes optimization modeling, computational methods, and their applications in electrical power systems and t...

We propose a risk-neutral second best toll pricing scheme to account for the possible nonuniqueness of user equilibrium solutions. The scheme is designed to optimize for the expected objective value as the UE solution varies within the solution set. We show that such a risk-neutral scheme can be formulated as a stochastic program, which complements...

Optimization techniques are used extensively for strategic and operations planning in a large number of system engineering applications. In the dairy farm industry, though development is of great interest and importance, analyzing and quantifying the benefits of manure separation can be a challenging task, usually because of the complex interacting...

In many applications, optimization of a collection of problems is required where each problem is structurally the same, but in which some or all of the data defining the instance is updated. Such models are easily specified within modern modeling systems, but have often been slow to solve due to the time needed to regenerate the instance, and the i...

Background/Question/Methods Trails Forward is a project in which we are developing a simulation environment that incorporates ecology, economics, and policy decisions to create a realistic and dynamic system which can be used to investigate a wide range of research questions. Central to this approach is the implementation of agent- or individual-...

In this article, we aim to find the most effective reformulation techniques to solve the MPCC (mathematical program with complementarity constraints) model that we proposed recently for continuous network design problems under asymmetric user equilibria. The MPCC model is based on a link-node nonlinear complementarity formulation for asymmetric use...

The April 2011 DOE workshop, 'Computational Needs for the Next Generation Electric Grid', was the culmination of a year-long process to bring together some of the Nation's leading researchers and experts to identify computational challenges associated with the operation and planning of the electric power system. The attached papers provide a journe...

We consider the approximation of a given m×n non-negative real matrix A by a weighted non-negative sum of binary matrices. Such approximation problems arise in intensity modulated arc therapy (IMAT), an advanced form of radiotherapy for cancer. In that context, the binary matrices Si represent the ‘open’ positions for the radiation beamlets in a so...

This document briefly describes GDXMRW, a suite of utilities to im-port/export data between GAMS and MATLAB (both of which the user is assumed to have already) and to call GAMS models from MATLAB and get results back in MATLAB. The software gives MATLAB users the ability to use all the optimization capabilities of GAMS, and allows visu-alization of...

We consider the system of m linear equations in n integer variables Ax=d and give sufficient conditions for the uniqueness of its integer solution x ∈ {−1, 1} n by reformulating the problem as a linear program. Necessary and sufficient uniqueness characterizations of ordinary linear programming solutions are utilized to obtain sufficient uniqueness...

Currently, there is a national push for a smarter electric grid, one that is more controllable and flexible. The full control of transmission assets are not currently built into electric network optimization models. Optimal transmission switching is a straightforward way to leverage grid controllability: to make better use of the existing system an...

In this article, we aim to find the most effective reformulation techniques to solve the MPCC (mathematical program with complementarity constraints) model that we proposed recently for continuous network design problems under asymmetric user equilibria. The MPCC model is based on a link-node nonlinear complementarity formulation for asymmetric use...

Extended mathematical programs are collections of functions and variables joined together using specific optimization and complementarity primitives. This paper outlines a mechanism to describe such an extended mathematical program by means of annotating the existing relationships within a model to facilitate higher level structure identification....

Existing second best toll pricing (SBTP) models determine optimal tolls of a subset of links in a transportation network by minimizing certain system objective, while the traffic flow pattern is assumed to follow user equilibrium (UE). We show in this paper that such toll design approach is risk prone, which tries to optimize for the best-case scen...

We describe a framework for modeling optimization problems for solution on a grid com- puter. The framework is easy to adapt to multiple grid engines, and can seamlessly integrate evolving mechanisms from particular computing platforms. It facilitates the widely used mas- ter/worker model of computing and is shown to be exible and powerful enough f...

Scheduling problems arise in many applications in process industries. However, despite various efforts to develop efficient scheduling methods, current approaches cannot be used to solve instances of industrial importance in reasonable time frames. The goal of this paper is the development of a dynamic decomposition scheme that exploits the structu...

This research aims enhancing the efficiency and reliability of PATH, the most widely used solver for mixed complementarity problems. A key component of the PATH algo-rithm is solving a series of linear complementary subproblems with a pivotal scheme. Improving the efficiency of the linear system routines (factor, solve, and update) re-quired by the...

The sample-path method is one of the most important tools in simulation- based optimization. The basic idea of the method is to approximate the ex- pected simulation output by the average of sample observations with a common random number sequence. In this paper, we describe a new variant of Powell's UOBYQA method, which integrates a Bayesian varia...

Production planning and scheduling problems routinely arise in process industries. In spite of extensive research work to develop efficient scheduling methods, existing approaches are inefficient in solving industrial-scale problems in reasonable time. In this paper we develop a dynamic decomposition scheme that exploits the structure of the proble...

In this paper, we propose a link-node complementarity model for the basic deterministic dynamic user equilibrium (DUE) problem with single-user-class and fixed demands. The model complements link-path formulations that have been widely studied for dynamic user equilibria. Under various dynamic network constraints, especially the exact flow propagat...

In this paper, we formulate the problem of finding an optimal generation dispatch and transmission topology to meet a specific inflexible load as a mixed integer program. Our model is a mixed-integer linear program because it employs binary variables to represent the state of the equipment and linear relationships to describe the physical system. W...

This talk will give a brief overview of the field of operations research (OR), and the models and tools that it can provide for radiation treatment planning. Some recent developments within OR and some future directions for the field will be outlined that have relevance for treatment planning.

We describe the application of a Bayesian variable-number sample-path (VNSP) optimization algorithm to yield a robust design for a floating sleeve antenna for hepatic microwave ablation. Finite element models are used to generate the electromagnetic (EM) field and thermal distribution in liver given a particular design. Dielectric properties of the...

DIRECT (Dividing RECTangles) is a deterministic global optimization algorithm for bound-constrained problems. The algorithm, based on a space-partitioning scheme, performs both global exploration and local exploitation. In this paper, we modify the deterministic DIRECT algorithm to handle noisy function optimization. We adopt a simple approach that...

In simulation-based optimization, we seek the optimal parameter settings that minimize or maximize certain performance measures of the simulation system. In this paper, we use a two-phase approach to calibrate simulation parameters using classification tools. This classification-based method is used in Phase I to facilitate the global search proces...

We investigate an on-line planning strategy for the fractionated radiotherapy planning problem, which incorporates the effects of day-to-day patient motion. On-line planning demonstrates significant improvement over off-line strategies in terms of reducing registration error, but it requires extra work in the replanning procedures, such as in the C...

An optimization framework for three-dimensional conformal radiation therapy is presented. In this type of therapy, beams of radiation are ap- plied to a patient from dieren t directions, where the aperture through which the beam is delivered from each direction is chosen to match the shape of the tumor, as viewed from that direction. Given a set of...

Eight years of progress towards the creation of a national health information network has resulted in a plethora of health data exchange relationships, most commonly called regional health information organizations (RHIOs). Various network types reflect both governance decisions and practical aspects, such as the need for a variety of information s...

We describe the solution of a bound constrained convex quadratic problem with limited memory resources. The problem arises from physical simulations occurring within video games. The motivating problem is outlined, along with a simple interior point approach for its solution. Various linear algebra issues arising in the implementation are explored,...

This text has grown over many years from a set of class notes for an undergraduate linear programming course offered at the University of Wisconsin-Madison. Though targeted to Computer Science undergraduates, the course has attracted both undergraduates and beginning graduate students from many other departments, including Industrial and Systems En...

Abstract A wide variety of optimization problems and techniques are used in radiation treatment planning. The problems typically involve large amounts of data, derived from simulations of patient anatomy and the properties of the delivery device. We investigate a three phase ap- proach for their solution based on sampling of the underlying data tha...

This paper formulates the continuous network design problem as a mathematical program with complementarity constraints (MPCC), with the upper level a nonlinear programming problem and the lower level a nonlinear complementarity problem. Unlike in most previous studies, the proposed framework is more general, in which both symmetric and asymmetric u...

Radiation therapy is extensively used to treat a wide range of cancers. Due to the increasing complexities of delivery mechanisms, and the improved imaging devices that allow more accurate determination of cancer location, determination of high quality treatment plans via trial-and-error methods is impractical and computer optimization approaches t...

Designing yacht rigs using empirical rules of thumb and large margins of safety can result in rigs that are substantially heavier than they need to be. We describe a suite of mathematical programming models for optimizing the dimensions and minimum scantlings of carbon-fibre rigs. By using mixed complementarity models the finite-element analysis of...

The continuous network design problem is formulated as a mathematical program with complementarity constraints (MPCC) and a Gauss-Seidel decomposition scheme is presented for the solution of the MPCC model. The model has an upper level as a nonlinear programming problem and the lower level as a nonlinear complementarity problem. With the applicatio...